In a known dosing pump with dosing piston-cylinder device and preliminary transport diaphragm, the preliminary transport chamber is connected to a dosed medium tank via a suction valve with a suction pipe and via a pressure valve with a return pipe. The preliminary transport occurs via the suction pipe and the suction valve to the preliminary transport chamber. The dosing piston takes the required quantity of dosed medium from the preliminary transport chamber. The surplus quantity of the dosed medium is transported back via the pressure valve and the return pipe into the dosed medium tank. The apparatus is relatively complicated because of the need to provide suction and pressure valves and a return pipe. In a known dosing pump, the pump cylinder is connectable via a pressure valve to a dosing station. When the piston emerges from the pump cylinder virtually an evacuation occurs, which leads to a gassing out of the dosed medium. In the case of certain dosed media, e.g. silicates, caustic soda solutions etc., this leads to crystallising out in the pump cylinder and hence to destruction of the dosing pump. With other dosed media such an evacuation leads to a polymerisation, and thus likewise to the destruction of the piston-cylinder device. Moreover, the provision of suction pipe and pressure pipe between preliminary transport chamber and dosed medium tank renders the bacteria-proof and gas-tight connection between dosing pump and dosed medium tank difficult.